In order to derive a simple numerical approximation scheme for \(\) , following [1]}, we consider a lower bound obtained by introducing two transportation plans. To further accelerate the method and enable GPU-friendly iterations, similarly to [2]}, [3]}, we consider an entropic regularization. We define for any \(\epsilon \ge 0\)
\(\begin{aligned}_\epsilon (, ) &\triangleq \inf _{\pi \in (\times )} _\epsilon (\pi ),\\\text{where} \qquad _\epsilon (\pi ) &\triangleq (\pi ) +\epsilon ^\otimes (\pi |\otimes ).\end{aligned}\) 
